Question

a biologist measures the height of a plant over several days. the table shows the plants growth. plant growth day (d) height in cm (h) 2 8.1 4 10.9 6 14.1 8 17.0 the data can be modeled with a linear best - fit equation. based on this equation, approximately how many more centimeters is the plant expected to grow between day 10 and day 11? 5 1.5 8.9 3.0

Explanation:

Step1: Calculate the slope (growth rate)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((2,8.1)\) and \((4,10.9)\). Then \(m=\frac{10.9 - 8.1}{4 - 2}=\frac{2.8}{2}=1.4\).

Step2: Interpret the slope

In a linear model \(h = md + b\) (where \(h\) is height, \(d\) is day), the slope \(m\) represents the rate of change of height with respect to days. The difference in height between day \(n\) and day \(n + 1\) is given by the slope of the linear best - fit equation.

Answer:

1.5 (Since the calculated slope \(m = 1.4\approx1.5\) which is the rate of growth per day, so the plant is expected to grow approximately \(1.5\) centimeters between Day 10 and Day 11)